Burger King agreed Thursday to sell itself to an investment firm with roots in Brazil in a deal valued at $4 billion, including the assumption of debt.

The deal is the largest leveraged buyout of a fast-food chain ever, according to the market researcher CapitalIQ, and the second for Burger King in the past eight years.

Burger King’s potential new owner, 3G Capital, decided on Burger King as a potential investment several months ago and began a series of friendly discussions with the fast-food chain’s management, people with direct knowledge of the talks said.

The investment firm plans to expand Burger King’s presence internationally, especially in Latin America and Asia.

“The iconic Burger King brand, its solid franchisee network and great product offerings make this a perfect fit for 3G Capital,” Alexandre Behring, 3G’s managing partner, said in a statement.

Yet in North America, where Burger King derives nearly 70 percent of its revenue, the chain has struggled. Last week, the company forecast weak demand in its new fiscal year and cautioned that uncertainty regarding the costs of wheat and beef could affect its results.

Analysts point to weaknesses like Burger King’s menu, which is less varied than McDonald’s. Burger King’s customers, largely younger men, have also suffered more from the economic slowdown.

On Thursday, Behring and Burger King’s chairman and chief executive, John Chidsey, spoke to Burger King employees in Miami about the deal, assuring them that 3G would continue to invest in the company.

Under the terms of the deal, 3G will pay $24 a share for Burger King, or $3.26 billion, a 46 percent premium to Burger King’s share price before reports emerged that the fast-food giant was in sales talks.

While some analysts questioned the price of the deal, Burger King’s stock had climbed as high as $22.06 as recently as April. 3G believes that the public markets have undervalued the company. Shares in Burger King jumped more than 25 percent Thursday, closing at $23.59.

One week before Burger King agreed to a sale, the volume of call options to buy the company’s stock jumped to 37,427, about 20 times the average of the previous four weeks, Bloomberg News reported.

3G expects to begin its tender offer no later than Sept. 17 and to close the deal in the fourth quarter this year. Burger King has the right to solicit higher offers through Oct. 12 under what is known as a “go shop” period.